Finite Group Databasebeta

← #25105156

Subgroups — #25105156

Order 11008.

1262 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583285C211yesmaximal, characteristic
2C2×#14583010C211yesmaximal, characteristic, complemented
3C2×#14583008C211yesmaximal, characteristic, complemented
4C2×#14583002C211yesmaximal, characteristic, complemented
5C2×#14583000C211yesmaximal, characteristic, complemented
6#19137159C211yesmaximal, characteristic, complemented
7#19137138C211yesmaximal, characteristic, complemented
8#19135461C211yesmaximal, characteristic, complemented
9#19135460C211yesmaximal, characteristic, complemented
10#19135452C211yesmaximal, characteristic, complemented
11#19135417C211yesmaximal, characteristic, complemented
12#19135408C211yesmaximal, characteristic, complemented
13#19134760C211yesmaximal, characteristic, complemented
14C4×#13063235C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C2×#13063321C2211yescharacteristic
20C2×#13063314C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×(C22⋊D43)⋊C4—22no—
26#14583285C418yescomplemented
27#14583010—24no—
28#14583008—24no—
29#14583002—24no—
30#14583000—24no—
31C2×#13063259C2211yescharacteristic
32C2×#13063258C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063235C2211yescharacteristic
41C2×#13063235C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×#13063235C2211yescharacteristic
44C2×C4×C43⋊C8C2211yescharacteristic
45#14582801C2211yescharacteristic
46#14582801C2211yescharacteristic
47#14582799—22no—
48#14582791—22no—
49#14582768C2211yescharacteristic
50#14582764C2211yescharacteristic
51#14582746—22no—
52C42×Dic43C2211yescharacteristic
53C22×SD16×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C22⋊D43—22no—
63C23×Dic43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884C2×C414yescomplemented
69C2×D344—22no—
70C2×D344—22no—
71C2×D344C2×C414yescomplemented
72C2×#10621882—22no—
73C2×#10621882—22no—
74C2×#10621882C2×C414yescomplemented
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77#13063321—22no—
78#13063321C2×C414yescomplemented
79#13063314—22no—
80#13063314C2×C414yescomplemented
81Q8×Dic43—22no—
82Q8×Dic43—22no—
83D4×Dic43—22no—
84D4×Dic43—22no—
85#13063287—22no—
86#13063287—22no—
87#13063287—22no—
88#13063287—22no—
89(C22⋊D43)⋊C4—48no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—22no—
94C2×C22⋊Dic43—21no—
95C2×(C2×D43)⋊C4—22no—
96C2×(C2×D43)⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43D412yes—
102C2×C4×Dic43D412yes—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105#13063259—22no—
106#13063258—22no—
107#13063256—22no—
108#13063249—22no—
109#13063247—22no—
110#13063247—22no—
111#13063246—22no—
112#13063245—22no—
113#13063245—22no—
114#13063235—22no—
115#13063235C2×C414yescomplemented
116#13063235D414yescomplemented
117#13063235D414yescomplemented
118C4×C43⋊C8—22no—
119C43⋊#95—22no—
120C22×Q8×C43C2311yescharacteristic
121C22×D4×C43C2311yescharacteristic
122C2×SD16×C43—22no—
123C2×SD16×C43—22no—
124C2×SD16×C43C2×C414yescomplemented
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—22no—
130C2×C42×C43C2311yescharacteristic
131#106×C43—22no—
132#103×C43—22no—
133#102×C43—22no—
134C4×C8×C43—22no—
135#95×C43—22no—
136C24×C43—21no—
137C23×D43—21no—
138C23×D43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43C22×C412yes—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C22×C412yes—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D412yes—
155C22×C4×C43C2411yescharacteristic
156C2×C22⋊D43—28no—
157C2×C22⋊D43—44no—
158C2×C22⋊D43—44no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—44no—
162C22×Dic43—42no—
163C22×Dic43C2×D412yes—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172C22×C412yes—
177C2×D172C22×C412yes—
178C2×C4×D43—44no—
179C2×C4×D43—44no—
180C2×C4×D43—42no—
181C2×C4×D43—42no—
182SD16×C43—28no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43C22×C412yes—
186C2×C8×C43C2×D412yes—
187C2×C8×C43C2×D412yes—
188C2×C8×C43#4112yes—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43—21no—
193C22⋊C4×C43—44no—
194C42×C43—21no—
195C42×C43—21no—
196C22⋊Dic43—42no—
197#10621884—28no—
198#10621882—28no—
199(C2×D43)⋊C4—28no—
200(C2×D43)⋊C4—44no—
201(C2×D43)⋊C4—44no—
202(C2×D43)⋊C4—42no—
203(C2×D43)⋊C4—42no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—42no—
209Dic43⋊C4—44no—
210C4×Dic43—24no—
211C4×Dic43—42no—
212C4×Dic43—42no—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C2×C43⋊C8C2×D412yes—
221C2×C43⋊C8C2×D412yes—
222C2×C43⋊C8#4112yes—
223D344—28no—
224C23×C43—22no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—42no—
228C23×C43—42no—
229C23×C43C22×D411yescharacteristic
230C22×D43—22no—
231C22×D43—22no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—42no—
237C22×D43—42no—
238C22×D43—42no—
239C22×D43—42no—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—41no—
243Q8×C43—41no—
244D4×C43—22no—
245D4×C43—22no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43AGL(1,ℤ/8)14yes—
258C2×C4×C43C23×C411yescharacteristic
259C2×C4×C43C22×D411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C22⋊D43—416no—
265C2×Dic43—22no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—22no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—84no—
274C2×Dic43C4×D414yes—
275C2×Dic43#12712yes—
276C2×Dic43#12712yes—
277D172—22no—
278D172—22no—
279D172—22no—
280D172—22no—
281D172—41no—
282D172—41no—
283D172—41no—
284D172—41no—
285C4×D43—84no—
286C4×D43—84no—
287C8×C43—22no—
288C8×C43C4×D414yescomplemented
289C43⋊C8—22no—
290C43⋊C8C4×D414yescomplemented
291#21701—431nomaximal, Sylow
292C22×C43—42no—
293C22×C43—44no—
294C22×C43—81no—
295C22×C43—81no—
296C22×C43—82no—
297C22×C43C2×C4×D411yescharacteristic
298C22×C43C2×#12711yescharacteristic
299C22×C43#53211yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)12yes—
301C22×C43#57512yes—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—44no—
305C2×D43—44no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—82no—
311C2×D43—82no—
312C4×C43—24no—
313C4×C43—42no—
314C4×C43—81no—
315C4×C43—81no—
316C4×C43C2×C4×D411yescharacteristic
317C4×C43C2×C4×D411yescharacteristic
318C4×C43#53211yescharacteristic
319C4×C43#53211yescharacteristic
320Dic43—22no—
321Dic43—22no—
322Dic43—24no—
323Dic43—81no—
324Dic43—81no—
325C2×#496—431no—
326C2×#442—431no—
327C2×#442—431no—
328C2×#440—431no—
329C2×#440—431no—
330C4×#127—431no—
331C4×#124—431no—
332#1970—431no—
333#1970—431no—
334#1968—431no—
335#1968D4311yescharacteristic, complemented
336#1961—431no—
337#1959—431no—
338#1847—431no—
339C4×#97—431no—
340C2×C43—82no—
341C2×C43C4×#12711yescharacteristic
342C2×C43C4×AGL(1,ℤ/8)12yes—
343C2×C43#315111yescharacteristic
344C2×C43#315311yescharacteristic
345C2×C43#318012yes—
346D43—82no—
347D43—82no—
348C22×SD16—431no—
349C22×SD16C2×D4311yescharacteristic
350C22×D8—431no—
351C22×D8—431no—
352C2×#127—431no—
353C2×#124—431no—
354C2×C4×Q8—431no—
355C2×C4×D4—431no—
356C2×C4×D4—431no—
357C2×C4×D4—431no—
358C2×C4×D4—862no—
359#496—438no—
360#442—864no—
361#442—864no—
362#440—864no—
363#440—864no—
364C2×#107—431no—
365C2×#107—431no—
366C2×#106—431no—
367C2×#106C2×D4311yescharacteristic
368C2×#103—431no—
369C2×#103C2×D4311yescharacteristic
370C2×#102—431no—
371C2×#102—431no—
372C2×#102—431no—
373C2×#102—431no—
374C2×#102—431no—
375C2×#102C2×D4311yescharacteristic
376C2×#97—431no—
377C2×#97—431no—
378C2×#97—431no—
379C2×#97—431no—
380C2×C4×C8—431no—
381C2×C4×C8C2×D4311yescharacteristic
382#391C2×D4311yescharacteristic
383#390—431no—
384#390—431no—
385#390—862no—
386#390C2×D4311yescharacteristic
387#388—862no—
388#384—431no—
389#382—431no—
390C4×C22⋊C4—862no—
391C43—431no—
392C43#2170111yescharacteristic, complemented, Sylow
393C22×Q8C22×D4311yescharacteristic
394C22×D4—431no—
395C22×D4—431no—
396C22×D4—862no—
397C22×D4C22×D4311yescharacteristic
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C2×SD16—22no—
402C2×SD16—22no—
403C2×SD16—434no—
404C2×SD16—862no—
405C2×SD16—862no—
406C2×SD16C4×D4314yescomplemented
407C2×D8—434no—
408C2×D8—434no—
409C2×D8—862no—
410C2×D8—862no—
411C2×D8—862no—
412C2×D8—862no—
413C22×C8—431no—
414C22×C8—431no—
415C22×C8C22×D4311yescharacteristic
416C22×C8C22×D4311yescharacteristic
417#127—434no—
418#127—862no—
419#124—434no—
420#124—862no—
421C4×Q8—862no—
422C4×Q8—862no—
423C4×D4—862no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—862no—
428C4×D4—862no—
429C4×D4—1728no—
430C2×C4⋊C4—431no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—22no—
437C2×C22⋊C4—862no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—862no—
442C2×C22⋊C4—862no—
443C2×C42—431no—
444C2×C42—431no—
445C2×C42—432no—
446C2×C42—432no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449#107—862no—
450#107—862no—
451#106—22no—
452#106—862no—
453#103—22no—
454#103—862no—
455#102—22no—
456#102—862no—
457#102—862no—
458#102—862no—
459#102—862no—
460#102—862no—
461#97—434no—
462#97—434no—
463#97—434no—
464#97—862no—
465C4×C8—22no—
466C4×C8—862no—
467#95—22no—
468#95—862no—
469C24—21no—
470C24—861no—
471C24—861no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C2×C4×D4312yes—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—868no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—1724no—
497C2×D4—1724no—
498C2×D4C2×C4×D4312yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—432no—
503C22×C4—431no—
504C22×C4—431no—
505C22×C4—861no—
506C22×C4—861no—
507C22×C4—1722no—
508C22×C4—1722no—
509C22×C4—1724no—
510C22×C4—1724no—
511C22×C4—1722no—
512C22×C4—1724no—
513C22×C4D4×D4312yes—
514C22×C4C23×D4311yescharacteristic
515SD16—28no—
516SD16—868no—
517D8—868no—
518D8—868no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—432no—
522C2×C8—432no—
523C2×C8—432no—
524C2×C8—432no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8C2×C4×D4312yes—
528C2×C8D4×D4312yes—
529C2×C8D4×D4312yes—
530C2×C8#1062190012yes—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—861no—
539C4⋊C4—1722no—
540C4⋊C4—1724no—
541C22⋊C4—44no—
542C22⋊C4—868no—
543C22⋊C4—1722no—
544C22⋊C4—1722no—
545C22⋊C4—1722no—
546C22⋊C4—1724no—
547C22⋊C4—1724no—
548C42—21no—
549C42—21no—
550C42—432no—
551C42—432no—
552C42—432no—
553C42—432no—
554C42—864no—
555C42—1722no—
556C42—1722no—
557C23—22no—
558C23—42no—
559C23—41no—
560C23—42no—
561C23—41no—
562C23—862no—
563C23—862no—
564C23—1722no—
565C23—1722no—
566C23—1721no—
567C23—1721no—
568C23—1722no—
569C23—1722no—
570C23—1721no—
571C23—1721no—
572C23C2×D4×D4311yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—862no—
582D4—862no—
583D4—862no—
584D4—862no—
585D4—17216no—
586D4—1721no—
587D4—1721no—
588D4—1721no—
589D4—1721no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—434no—
600C2×C4—432no—
601C2×C4—432no—
602C2×C4—862no—
603C2×C4—862no—
604C2×C4—862no—
605C2×C4—862no—
606C2×C4—3444no—
607C2×C4—3444no—
608C2×C4—3444no—
609C2×C4—1722no—
610C2×C4—1722no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4#1306335214yes—
614C2×C4C22×C4×D4311yescharacteristic
615C2×C4C2×D4×D4311yescharacteristic
616C2×C4C2×D4×D4311yescharacteristic
617C2×C4#41×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C8—22no—
621C8—434no—
622C8—862no—
623C8(C22⋊D43)⋊C414yescomplemented
624C22—42no—
625C22—44no—
626C22—82no—
627C22—81no—
628C22—81no—
629C22—3442no—
630C22—3442no—
631C22—3441no—
632C22—3441no—
633C22—3441no—
634C22—3441no—
635C22—1722no—
636C22—1722no—
637C22—1724no—
638C22—1724no—
639C22C4×D4×D4311yescharacteristic
640C22#127×D4311yescharacteristic
641C22#1458344411yescharacteristic
642C22C2×#1306335212yes—
643C22#1458369612yes—
644C4—24no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—862no—
649C4—862no—
650C4—864no—
651C4—3441no—
652C4—3441no—
653C4C4×D4×D4311yescharacteristic
654C4C2×(C22⋊D43)⋊C411yescharacteristic
655C4#1458344411yescharacteristic
656C4#1458344811yescharacteristic
657C2—82no—
658C2—3442no—
659C2—3442no—
660C2#1913715911yescharacteristic
661C2C4×#1306335212yes—
662C2#1914504211yescharacteristic
663C2#1914505611yescharacteristic
664C2#1914528612yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC2×#14583285C2
cosocleC22×C4×C43C24
hypercenter#1968D43
hypocenterC43#21701
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583010C2semidirect
3. C2×#14583008C2semidirect
4. C2×#14583002C2semidirect
5. C2×#14583000C2semidirect
6. #19137159C2semidirect
7. #19137138C2semidirect
8. #19135461C2semidirect
9. #19135460C2semidirect
10. #19135452C2semidirect
11. #19135417C2semidirect
12. #19135408C2semidirect
13. #19134760C2semidirect
14. C4×#13063235C2semidirect
15. C43×#1968C2semidirect
26. #14583285C4semidirect
68. C2×#10621884C2×C4semidirect
71. C2×D344C2×C4semidirect
74. C2×#10621882C2×C4semidirect
78. #13063321C2×C4semidirect
80. #13063314C2×C4semidirect
115. #13063235C2×C4semidirect
116. #13063235D4semidirect
117. #13063235D4semidirect
124. C2×SD16×C43C2×C4semidirect
288. C8×C43C4×D4semidirect
290. C43⋊C8C4×D4semidirect
335. #1968D43semidirect
392. C43#21701semidirect
406. C2×SD16C4×D43semidirect
623. C8(C22⋊D43)⋊C4semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145832852
C2×#145830102
C2×#145830082
C2×#145830022
C2×#145830002
#191371592
#191371382
#191354612
#191354602
#191354522
#191354172
#191354082
#191347602
C4×#130632352
C43×#19682
#2170143